In the first chapter, Machiavelli begins to lay out his typology of regimes (quick aside, when the chapter is short, we will quote it in full; otherwise, you will need to refer to your own copy of the text):
How Many Are the Kinds of Principalities and in What Modes They Are Acquired
All states, all dominions that have held and do hold empire over men have been and are either republics or principalities. The principalities are either hereditary, in which the bloodline of their lord has been their prince for a long time, or they are new. The new ones are either altogether new, as was Milan to Francesco Sforza, or they are like members added to the hereditary state of the prince who acquires them, as is the kingdom of Naples to the king of Spain. Dominions so acquired are either accustomed to living under a prince or used to being free; and they are acquired either with the arms of others or with one's own, either by fortune or by virtue.
Generally there are two types: republics and principalities. This can be compared to both Aristotle and Plato’s typologies: monarchy, aristocracy, politea, democracy, oligarchy, and tyranny, on the one hand; and kingship, aristocracy, timocracy, oligarchy, democracy, and tyranny on the other.